631 research outputs found
On U_q(SU(2))-symmetric Driven Diffusion
We study analytically a model where particles with a hard-core repulsion
diffuse on a finite one-dimensional lattice with space-dependent, asymmetric
hopping rates. The system dynamics are given by the
\mbox{U[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic
Heisenberg antiferromagnet. Exploiting this symmetry we derive exact
expressions for various correlation functions. We discuss the density profile
and the two-point function and compute the correlation length as well
as the correlation time . The dynamics of the density and the
correlations are shown to be governed by the energy gaps of a one-particle
system. For large systems and depend only on the asymmetry. For
small asymmetry one finds indicating a dynamical exponent
as for symmetric diffusion.Comment: 10 pages, LATE
Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
The reaction process is modelled for ballistic reactants on an
infinite line with particle velocities and and initially
segregated conditions, i.e. all A particles to the left and all B particles to
the right of the origin. Previous, models of ballistic annihilation have
particles that always react on contact, i.e. pair-reaction probability .
The evolution of such systems are wholly determined by the initial distribution
of particles and therefore do not have a stochastic dynamics. However, in this
paper the generalisation is made to , allowing particles to pass through
each other without necessarily reacting. In this way, the A and B particle
domains overlap to form a fluctuating, finite-sized reaction zone where the
product C is created. Fluctuations are also included in the currents of A and B
particles entering the overlap region, thereby inducing a stochastic motion of
the reaction zone as a whole. These two types of fluctuations, in the reactions
and particle currents, are characterised by the `intrinsic reaction rate', seen
in a single system, and the `extrinsic reaction rate', seen in an average over
many systems. The intrinsic and extrinsic behaviours are examined and compared
to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte
Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
The one-dimensional partially asymmetric simple exclusion process with open
boundaries is considered. The stationary state, which is known to be
constructed in a matrix product form, is studied by applying the theory of
q-orthogonal polynomials. Using a formula of the q-Hermite polynomials, the
average density profile is computed in the thermodynamic limit. The phase
diagram for the correlation length, which was conjectured in the previous
work[J. Phys. A {\bf 32} (1999) 7109], is confirmed.Comment: 24 pages, 6 figure
Will jams get worse when slow cars move over?
Motivated by an analogy with traffic, we simulate two species of particles
(`vehicles'), moving stochastically in opposite directions on a two-lane ring
road. Each species prefers one lane over the other, controlled by a parameter
such that corresponds to random lane choice and
to perfect `laning'. We find that the system displays one large cluster (`jam')
whose size increases with , contrary to intuition. Even more remarkably, the
lane `charge' (a measure for the number of particles in their preferred lane)
exhibits a region of negative response: even though vehicles experience a
stronger preference for the `right' lane, more of them find themselves in the
`wrong' one! For very close to 1, a sharp transition restores a homogeneous
state. Various characteristics of the system are computed analytically, in good
agreement with simulation data.Comment: 7 pages, 3 figures; to appear in Europhysics Letters (2005
A Position-Space Renormalization-Group Approach for Driven Diffusive Systems Applied to the Asymmetric Exclusion Model
This paper introduces a position-space renormalization-group approach for
nonequilibrium systems and applies the method to a driven stochastic
one-dimensional gas with open boundaries. The dynamics are characterized by
three parameters: the probability that a particle will flow into the
chain to the leftmost site, the probability that a particle will flow
out from the rightmost site, and the probability that a particle will jump
to the right if the site to the right is empty. The renormalization-group
procedure is conducted within the space of these transition probabilities,
which are relevant to the system's dynamics. The method yields a critical point
at ,in agreement with the exact values, and the critical
exponent , as compared with the exact value .Comment: 14 pages, 4 figure
Electronic correlation effects and the Coulomb gap at finite temperature
We have investigated the effect of the long-range Coulomb interaction on the
one-particle excitation spectrum of n-type Germanium, using tunneling
spectroscopy on mechanically controllable break junctions. The tunnel
conductance was measured as a function of energy and temperature. At low
temperatures, the spectra reveal a minimum at zero bias voltage due to the
Coulomb gap. In the temperature range above 1 K the Coulomb gap is filled by
thermal excitations. This behavior is reflected in the temperature dependence
of the variable-range hopping resitivity measured on the same samples: Up to a
few degrees Kelvin the Efros-Shkovskii ln law is obeyed,
whereas at higher temperatures deviations from this law are observed,
indicating a cross-over to Mott's ln law. The mechanism of
this cross-over is different from that considered previously in the literature.Comment: 3 pages, 3 figure
Transport of interface states in the Heisenberg chain
We demonstrate the transport of interface states in the one-dimensional
ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis
is based on the standard Adiabatic Theorem. This is supplemented by a numerical
analysis via the recently developed time dependent DMRG method, where we
calculate the adiabatic constant as a function of the strength of the magnetic
field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure
Remarks on the multi-species exclusion process with reflective boundaries
We investigate one of the simplest multi-species generalizations of the one
dimensional exclusion process with reflective boundaries. The Markov matrix
governing the dynamics of the system splits into blocks (sectors) specified by
the number of particles of each kind. We find matrices connecting the blocks in
a matrix product form. The procedure (generalized matrix ansatz) to verify that
a matrix intertwines blocks of the Markov matrix was introduced in the periodic
boundary condition, which starts with a local relation [Arita et al, J. Phys. A
44, 335004 (2011)]. The solution to this relation for the reflective boundary
condition is much simpler than that for the periodic boundary condition
An Extended Network Model with a Packages Diffusion Process
The dynamics of a packages diffusion process within a selforganized network
is analytically studied by means of an extended % -spin facilitated kinetic
Ising model (Fredrickson-Andersen model) using a Fock-space representation for
the master equation. To map the three component system (active, passive and
packages cells) onto a lattice we apply two types of second quantized
operators. The active cells correspond to mobile states whereas the passive
cells correspond to immobile states of the Fredrickson-Andersen model. An
inherent cooperativity is included assuming that the local dynamics and
subsequently the local mobilities are restricted by the occupation of
neighboring cells. Depending on a temperature-like parameter
(interconnectivity) the diffusive process of the packages (information) can be
almost stopped, thus we get a well separation of the time regimes and a
quasi-localization for the intermediate range at low temperatures.Comment: 13 pages and 1 figur
Phase diagram of a generalized ABC model on the interval
We study the equilibrium phase diagram of a generalized ABC model on an
interval of the one-dimensional lattice: each site is occupied by a
particle of type \a=A,B,C, with the average density of each particle species
N_\a/N=r_\a fixed. These particles interact via a mean field
non-reflection-symmetric pair interaction. The interaction need not be
invariant under cyclic permutation of the particle species as in the standard
ABC model studied earlier. We prove in some cases and conjecture in others that
the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique
density profile \p_\a(x) except for some special values of the r_\a for
which the system undergoes a second order phase transition from a uniform to a
nonuniform periodic profile at a critical temperature .Comment: 25 pages, 6 figure
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